That is a great question. Very simple question, but difficult to answer. Related question: ruthenium is just above Os in the periodic table, but RuO4 will oxidize alkynes to diketones whereas OsO4 does not. Why?
The best I can find is this paper, which covers alkenes (not alkynes). The gist of it is that Os is more stable at higher oxidation states (e.g. Os(VIII), Os(VI) ) relative to smaller elements such as Ru and presumably Mn.
RuO4 is more similar in many respects to KMnO4 than it is to OsO4 – will do many of the same reactions, even though they are not even in the same column of the periodic table.

I suppose the best answer I can give you is that chemistry is as yet an incomplete science, and there are some questions we are still trying to figure out the answers to.

Alkynes are generally less electron-rich than alkenes, owing to the larger electronegativity of sp hybridized carbon atoms. Electrophilic reagents like ozone, HX and OsO4 tend to react more slowly with alkynes.

Regarding why OsO4 doesn’t work, I’m not entirely sure.

Thanks for digging through the literature, Jon. Much appreciated.

For what it’s worth, I cannot find the first reaction (oxidation of diphenylacetylene to benzil with osmium tetroxide) on Reaxys. Quite a variety of oxidants have been used for this particular substrate, including KMnO4 which is perhaps more familiar to undergrads (JOC 1989 5182), but not OsO4.

The second substrate is even more dubious. There is only one report of this transformation (TL 2004 8575) using trifluoro DMDO, not OsO4, and the authors report that the 1,2-diketone was only a side product, obtained in 18% yield (the main product being that with the hydroxyls oxidised to carbonyls). I don’t know where the “OsO4/KClO3” comes from, but it’s not in the primary literature.

Alkynes CAN be cyclopropanated, it’s just that this topic almost never comes up in introductory organic chemistry.

this paper also show cyclopropanation of an alkyne.

That is new to me.

This didn’t appear in my copy of March, nor any other book in my collection, and I don’t have Scifinder at my fingertips anymore to really dig into the literature.

I’d need to see the primary literature to know the exact conditions for the reaction. It’s very possible to selectively dihydroxylate an alkene in the presence of an alkyne; reactions with alkynes are much slower.

Thanks for adding this.

When does it work, and when doesn’t it?